Incorporated herewithin by reference is an article "Subband Coding of Images" by J. W. Woods and S. D. O'Neil appearing in pages 1278-1288 of IEEE TRANSACTIONS ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, Vol. ASSP-34, No. 5, October 1986. Woods and O'Neil describe a filter tree branching four ways at each successive node in the tree structure. This filter tree is used for decomposing an image into components enhibiting reduced degrees of randomness in their samples, as a step in an entropic coding procedure.
Entropy is a measure of the degree of randomness of a set of random variables in the xsamples of a code stream. Entropic coding reduces code lengths by reducing the degree of randomness in a stream of samples so it can be encoded in a more efficient manner. Dissection of data by filtering is a typical procedure for reducing randomness in data. In entropic coding it is also typical to use differential pulse code modulation (DPCM) to reduce the degree of randomness in picture-element (pixel) samples. It is also typical in entropic coding to include a final step of run-length coding or of variable-length statistical coding, such as Huffman coding.
At each node in the Woods and O'Neil filtering tree, a description of image samples from the trunk or a major branch of the filter tree is decomposed by four branch processes. In these processes the description of image samples received at the node from which the branches stem is convolved with the responses of a set of four filters that are two-dimensional quadrature mirror filters (QMFs). The first, second, third and fourth filters of the QMF set respectively low-pass-filter in both first and second orthogonal dimensions of image space, low-pass-filter in that first dimension and high-pass-filter in that second dimension, high-pass-filter in that first dimension and low-pass-filter in that second dimension, and high-pass-filter in both those first and second dimensions. These filter responses are in effect each subjected to successive decimations, first in the first dimension and then in the second dimension, to generate the image samples supplied at the following four subnodes of the filter tree. Each of the resulting subbands is divided into at least quarters by an iteration of the quadrature mirror filtering and the two-dimensional decimation procedure already described.